Question

What is the inverse of h? h(x) = 6x 1

Answer 1

H(x) = 6x + 1
y = 6x + 1
6x = y - 1
x = (y - 1)/6

Inverse is h^-1(x) = (x - 1)/6

Answer 2

Answer:

The inverse of h(x) is $h^{-1}(x)\,=\,\frac{log\,6x}{log\,6}$

Step-by-step explanation:

Given: h function, h(x) = $6^{x-1}$

To find: Inverse of h function.

We are given h function in terms of x. So we equate this function with arbitrary element say y, then convert the given function of x in terms of y.

The function we obtained in term of y is the required inverse function of h.

Consider,

y = h(x)

$y\,=\,6^{x-1}$

Take log on both sides, we get

$log\,y\,=\,log\,6^{x-1}$

now we use rule of logarithmic function in RHS, $log\,m^n\,=\,n\,log\,m$ , we get

$log\,y\,=\,(x-1)\,log\,6$

$x-1\,=\,\frac{log\,y}{log\,6}$

$x\,=\,\frac{log\,y}{log\,6}+1$

$x\,=\,\frac{log\,y+log\,6}{log\,6}$

Now using another rule of logarithmic function $log\,mn\,=\,log\,m+\,log\,n$ we get

$x\,=\,\frac{log\,6y}{log\,6}$

Therefore, The inverse of h(x) is $h^{-1}(x)\,=\,\frac{log\,6x}{log\,6}$