Question

metry Precalculus Honors S1Understanding the Inverse Relationshiphe table shows the inputs and corresponding outputsor the function f(x) = (1)(2)*.026x84.Find the following values of the function.ƒ^¹ (3)=[f-¹ (8) =

Answer 1

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SOLUTION

`\begin{gathered} f(x)=((1)/(8))2^x \\ f^(-1)(x)=? \end{gathered}`

To determine the inverse function;

`Solve\text{ the equation for x, then interchange x for y.}`
`Let\text{ y=f\lparen x\rparen}`
`\begin{gathered} y=(1)/(8)(2)^x \\ 8y=2^x \\ ln(8y)=ln2^x \\ ln(8y)=xln2 \\ x=(ln(8y))/(ln2)\text{ ie y=}(ln(8x))/(ln2) \\ \therefore f^(-1)(x)=(ln(8x))/(ln(2)) \end{gathered}`

Now,

`f^(-1)((1)/(2))=(ln(8*(1)/(2)))/(ln2)=(ln4)/(ln2)=2`
`f^(-1)(8)=(ln(8*8))/(ln2)=(ln(64))/(ln2)=6`