Question

Write the inverse of h(x) = e 2x h -1(x) = log e2 x 2log ex ½log ex

Answer 1

Answer:

C

Step-by-step explanation:

So we have the function:

$h(x)=e^{2x}$

To find the inverse, switch h(x) and x, change h(x) to h⁻¹(x), and solve for it. Thus: "

$x=e^{2h^{-1}(x)}$

So, take the natural log (log to base e) of both sides:

$\ln(x)=\ln(e^{2h^{-1}(x)})$

The right side will cancel:

$\ln(x)=2h^{-1}(x)$

Divide both sides by 2:

$h^{-1}(x)=\frac{1}{2}\ln(x)$

And we're done!

Our answer is C

Note:

$\ln(x)=\log_ex$