Finding the inverse of a function | Maths | Quizalize & Oak National Academy

Starter quiz

If the vertical axis is labelled 'Range', what is the missing word on the horizontal axis?

Domain ✓

Range

Input

Output

$x$ -axis
For the linear equation $y=7(x-12)$ what is the value of the $y$ coordinate if $x=6$ ?

'-42' ✓
For the linear equation $y=7(x-12)$ what is the value of the $x$ coordinate if $y=35$ ?

'17' ✓
Which of the below makes $a$ the subject of the equation $7a+3=b$ ?

$a={{b-3}\over{7}}$ ✓

$a=7b+3$

$a={{b+3}\over{7}}$

$a={{b}\over{7}}-3$
Which of the below makes $a$ the subject of the equation ${1\over2}(5a-7)=b$ ?

${1\over2}(5b-7)=a$

$a={{2b-7}\over{5}}$

$a={{2b+7}\over{5}}$ ✓

$a={{2b}\over{5}}-7$

$a={{5b+7}\over{2}}$
Why is this function not valid?

There is a one-to-one relationship

There is a many-to-one relationship

There is a many-to-many relationship

There is a one-to-many relationship ✓

${\text{f}}(x)$ is shorthand notation for a function of $x$ . ${\text{f}}^{-1}(x)$ is shorthand notation for its ...

reverse function

inverse function ✓

reciprocal function
If ${\text{f}}(x)=8x+2$ what was the value of $x$ that mapped to $34$ ?

'4' ✓
Which of the below is the inverse function of ${\text{f}}(x)=7x$ ?

${\text{f}}(x)={x\over7}$

$-{\text{f}}(x)={x\over7}$

${\text{f}}^{-1}(x)={x\over7}$ ✓

${\text{f}}^{-1}(x)={7\over{x}}$
If ${\text{f}}(17)=391$ then ${\text{f}}^{-1}(391)=$ ______.

'17' ✓
Match the functions to their inverses.

${\text{f}}(x)=4x+5$

⇔

${\text{f}}^{-1}(x)={{x-5}\over{4}}$ ✓

${\text{f}}(x)=4x-5$

⇔

${\text{f}}^{-1}(x)={{x+5}\over{4}}$ ✓

${\text{f}}(x)=4(x+5)$

⇔

${\text{f}}^{-1}(x)={{x}\over{4}}-5$ ✓

${\text{f}}(x)=5x+4$

⇔

${\text{f}}^{-1}(x)={{x-4}\over{5}}$ ✓

${\text{f}}(x)=5(x+4)$

⇔

${\text{f}}^{-1}(x)={{x}\over{5}}-4$ ✓
A function and its inverse are a reflection of one another in the line...

$y={\text{f}}(x)$

$y=x$ ✓

${\text{f}}^{-1}(x)={\text{f}}(x)$

of the $x$ axis

of the $y$ axis

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Confusing domain and range when considering the inverse function.

The range of a function is the domain of its inverse function.

Inverse function - An inverse function reverses the mapping of the original function.