All 303 families

GB-41-01-001 · Inverse functions

The function f is defined by f(x)=7x−4f(x)=7x-4. Find f−1(x)f^{-1}(x).

Inverse Functions Booklet p. 31
Method
1) Write as y = f(x)
2) Swap x and y
3) Rearrange to make y the subject
4) Write the inverse function
Worked Example (GB-41-01-001)
1)
Write the function as y=7x−4y=7x-4.
2)
Swap x and y: x=7y−4x=7y-4.
3)
Rearrange to make y the subject: x+4=7y⇒y=x+47x+4=7y\Rightarrow y=\frac{x+4}{7}.
4)
Write the inverse: f−1(x)=x+47f^{-1}(x)=\frac{x+4}{7}.
Ans = f−1(x)=x+47f^{-1}(x)=\frac{x+4}{7}