If h(x) = (fog) (x) and h(x) = 4 square root x+7, find g(x) if f(x) = 4 square root x+ 1

is the answer

given

and .

Step-by-step explanation:

Inputting the given function for h(x)  into the above:

Now we are plugging in g(x) for x in the expression for f which is which gives us :

We want to solve this for g(x).

If you don't like the looks of g(x) (if you think it is too daunting to look at), replace it with u and solve for u.

Divide both sides by 4:

Square both sides:

Subtract 1 on both sides:

Simplify left hand side:

Remember u was g(x) so you just found g(x) so congratulations.

.

Let's check it:

I replace g(x) with x+6 since g(x)=x+6.

I replace x in f with (x+6).

The check is done. We have that .

i just took the test, the correct answer is .. 31.5 in.