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A function $g(x)$ is defined on $ extbf{R}$, the set of real numbers, by $g(x) = \frac{1}{5}x - 4.$ Find the inverse function, $g^{-1}(x)$. - Scottish Highers Maths - Question 2 - 2018

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Question 2

A-function-$g(x)$-is-defined-on-$-extbf{R}$,-the-set-of-real-numbers,-by---$g(x)-=-\frac{1}{5}x---4.$---Find-the-inverse-function,-$g^{-1}(x)$.-Scottish Highers Maths-Question 2-2018.png

A function $g(x)$ is defined on $ extbf{R}$, the set of real numbers, by $g(x) = \frac{1}{5}x - 4.$ Find the inverse function, $g^{-1}(x)$.

Worked Solution & Example Answer:A function $g(x)$ is defined on $ extbf{R}$, the set of real numbers, by $g(x) = \frac{1}{5}x - 4.$ Find the inverse function, $g^{-1}(x)$. - Scottish Highers Maths - Question 2 - 2018

Step 1

Step 1: Equate Composite Function to x

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Answer

To find the inverse function, we start by setting the function equal to xx:
g−1(x)=15g(x)−4=xg^{-1}(x) = \frac{1}{5}g(x) - 4 = x

Step 2

Step 2: Rearrange to Express x in terms of g^{-1}(x)

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Answer

Rewrite the equation:
15g−1(x)−4=x\frac{1}{5}g^{-1}(x) - 4 = x
Add 4 to both sides:
15g−1(x)=x+4\frac{1}{5}g^{-1}(x) = x + 4
Multiply both sides by 5:
g−1(x)=5(x+4)g^{-1}(x) = 5(x + 4)

Step 3

Step 3: State the Inverse Function

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Answer

Thus, we state the inverse function as:
g−1(x)=5x+20g^{-1}(x) = 5x + 20

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