Question

Use the function f(x)=123x−2f(x)=123x−2 to answer the questions. A: What is f−1(x)f−1(x)? B: What should be done to find the value of xx that makes f(x)=0.75f(x)=0.75? C: For what value of xx does f(x)=0.75f(x)=0.75?

Answer 1

Answer:

1) $f^{-1}(x)=\frac{x+2}{123}$

2) $f(0.02235)=0.75$

3) $x=0.02235$

Explanation:

Part 1)

Given that

$f(x)=123x-2$

To find $f^{-1}(x)$ we put $x=f^{-1}(x)$ in the given function to obtain

$f(f^{-1}(x))=123\times f^{-1}(x)-2\\\\\Rightarrow x=123\times f^{-1}(x)-2(\because f(f^{-1}(x)=x)\\\\\therefore f^{-1}(x)=\frac{x+2}{123}$

Part 2 and 3)

for $f(x)=0.75$ we put f(x) = 0.75 and then solve for 'x'

$0.75=123\times x -2\\\\\therefore x=\frac{0.75+2}{123}=0.02235$