Functions and function notation

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शिक्षकों के लिए: Functions and function notation (Mathematics, Algebra) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके शिक्षार्थी लाइव गेम की तरह खेलें।

लेसन नोट्स स्लाइड्स प्रैक्टिस सवाल

लेसन नोट्स

What a function is

A function is a rule that takes an input and gives exactly one output. A function machine shows the steps.
Function notation: f(x) = 3x + 2 means "the function f acts on x". Read f(x) as "f of x", not f times x.
To evaluate f(4), replace x with 4: f(4) = 3(4) + 2 = 14.

Composite functions

fg(x) means "do g first, then f": fg(x) = f(g(x)).
If f(x) = 2x and g(x) = x + 3, then fg(x) = 2(x + 3) = 2x + 6, but gf(x) = 2x + 3. The order matters.

Composition: g first, then f

Inverse functions

The inverse function f^-1(x) reverses f. To find it: write y = f(x), swap x and y, then rearrange for y.
If f(x) = 2x + 5, then x = 2y + 5, so y = \frac{x - 5}{2} and f^-1(x) = \frac{x - 5}{2}.
f^-1(f(x)) = x: applying a function and its inverse returns the starting value.
An inverse must return exactly one input for each output. For example, x² needs a domain restriction such as x ≥ 0 to have inverse √x.

Domain and range

The domain is the set of allowed inputs; the range is the set of possible outputs.
f(x) = \frac{1}{x} cannot take x = 0, and f(x) = \√{x} needs x \geq 0.

Solving using functions

To solve f(x) = 11 when f(x) = 3x + 2, write 3x + 2 = 11, so x = 3.

स्लाइड्स

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 33 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

1.In function notation, what does f(x) mean?
Easy
- Af multiplied by x
- BThe output of function f for input x
- CThe factors of x
- Df divided by x
2.If f(x) = 2x + 3, what is f(4)?
Easy
- A8
- B11
- C14
- D24
3.If f(x) = x² - 1, what is f(5)?
Easy
- A9
- B24
- C26
- D4
4.If f(x) = 10 - x, what is f(-2)?
Easy
- A8
- B12
- C-8
- D-12
5.If f(x) = 4x, what is f(x + 1)?
Easy
- A4x + 1
- B4x + 4
- C4x
- Dx + 4
6.If f(x) = 3x + 2 and f(a) = 14, what is a?
Easy
- A4
- B5.33
- C12
- D3
7.If f(x) = 2x and g(x) = x + 3, what is fg(x)?
Easy
- A2x + 3
- B2x + 6
- C2x² + 3
- Dx + 6
8.If f(x) = 2x and g(x) = x + 3, what is gf(x)?
Easy
- A2x + 3
- B2x + 6
- C2x² + 3
- Dx + 6

और सवाल

9.If f(x) = x + 4 and g(x) = 3x, what is fg(2)?
Medium
- A10
- B18
- C6
- D14
10.If f(x) = x² and g(x) = x - 3, what is gf(4)?
Medium
- A1
- B13
- C25
- D16
11.Find f^-1(x) when f(x) = x + 7.
Medium
- Ax + 7
- Bx - 7
- C7 - x
- D\frac{x}{7}
12.Find f^-1(x) when f(x) = 2x + 5.
Medium
- A\frac{x - 5}{2}
- B\frac{x}{2} + 5
- C2x - 5
- D\frac{x + 5}{2}
13.Find f^-1(x) when f(x) = \frac{x}{3} - 2.
Medium
- A3x + 2
- B3(x + 2)
- C3x - 2
- D\frac{x + 2}{3}
14.If f(x) = 3x - 1, what is f^-1(8)?
Medium
- A23
- B3
- C2.33
- D1
15.For f(x) = 2/x with nonzero real inputs, find the inverse function.
Medium
- A\frac{x}{2}
- B\frac{2}{x}
- C-\frac{2}{x}
- D2x
16.Which value of x cannot be used in f(x) = \frac{1}{x - 3}?
Easy
- A0
- B1
- C3
- D-3
17.What is the domain restriction of f(x) = \√{x} for real outputs?
Easy
- Ax > 0 only
- Bx \geq 0
- Cx \leq 0
- Dnone
18.If f(x) = x² + 1, what is the range for real x?
Medium
- Af(x) \geq 0
- Bf(x) \geq 1
- Cf(x) \leq 1
- Dall numbers
19.If f has an inverse function and x is in its domain, what is f⁻¹(f(x)) equal to?
Easy
- A0
- B1
- Cx
- Df(x)
20.If f(x) = 2x + 1 and g(x) = x², solve fg(x) = 19.
Medium
- Ax = \pm 3
- Bx = 3 only
- Cx = \pm 9
- Dx = 9
21.A function machine multiplies by 3, then subtracts 4. Which function is it?
Medium
- Af(x) = 3(x - 4)
- Bf(x) = 3x - 4
- Cf(x) = 3 - 4x
- Df(x) = 3x + 4
22.What is the inverse of a function machine step 'multiply by 5'?
Easy
- AMultiply by 5
- BAdd 5
- CDivide by 5
- DSubtract 5
23.If f(x) = x², what is f(-3)?
Medium
- A-9
- B9
- C6
- D-6
24.If f(x) = 5 - 2x, what is f^-1(x)?
Medium
- A\frac{5 - x}{2}
- B\frac{x - 5}{2}
- C5 - \frac{x}{2}
- D\frac{x + 5}{2}
25.Which of these is a function?
Easy
- AOne input giving two outputs
- BOne input giving exactly one output
- CTwo inputs giving no output
- DAn equation with no variable
26.f(x) means f multiplied by x.
Easy
True or false?
27.fg(x) means apply g first and then f.
Easy
True or false?
28.fg(x) always equals gf(x).
Easy
True or false?
29.The inverse of f(x) = x - 5 is f^-1(x) = x + 5.
Easy
True or false?
30.f(x) = \frac{1}{x} is defined at x = 0.
Medium
True or false?
31.Which of these are correct for f(x) = 2x + 1?
Medium
- Af(3) = 7
- Bf(0) = 0
- Cf(-1) = -1
- Df^-1(x) = \frac{x - 1}{2}
- Ef(2) = 6
32.Which value is excluded from the domain of f(x) = \frac{1}{x - 2}?
Medium
- Ax = 2
- Bx = 0
- Cx = 1
- Dx = -2
33.Find the inverse of f(x) = 4x - 3, showing the method.
Medium

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