Question

Someone help me with this question ASAP and show work please and thank you

Answer 1

Explanation:

g(f(x)) means that wherever you see an x in g(x) you put f(x) in it's place. Read that sentence a couple of times until it makes sense.

g(x) = (x + 1)/-4

g(f(x)) = (f(x) + 1) / - 4 Now wherever you see f(x), put in -4x - 1

g(f(x)) = [(-4x - 1) + 1] / - 4 Remove ( )

g(f(x)) = [-4x - 1 + 1 ] / - 4

g(f(x)) = [-4x] / - 4 Do the division

g(f(x)) = x

Neat problem. thanks for posting.

Answer 2

g(f(x)) = x

Explanation:

You are given f(x) = -4x - 1 and g(x) =
`(x+1)/(-4)`. Keep in mind that f(x) or g(x) is the same as a y = equation, but two separate equations.

You are trying to find g(f(x)), which means that you will use f(x) and substitute this value into the x value in the equation of g(x).

It will look like: g(-4x - 1) =
`(x+1)/(-4)`

`((-4x-1)+1)/(-4)`

Now evaluate the expression to solve the problem. Start by combining like terms.

`((-4x))/(-4)`

You are left with -4x/-4. We can simplify this even further by dividing both sides of the fraction by -4/-4. The -4's cancel out and become 1's, so you are left with:

`x`