Write h(f(x)) as an expression in terms of x

Question

f(x) = (3x-5)^3

h(x) = 2 3√x +8

h(f(x)) = Answer

Answer 1

Hello Mike!

If I understand you correctly, h(x) = 2 *( ³√x) + 8.

If that is the case, then this question is asking you to plug f(x) (which is (3x - 5)³) into h(x) wherever there is an x.

So h(f(x)) would be written as h(f(x)) = 2 *( ³√(3x - 5)³)) + 8

Since we have a cubic binomial (two terms that are being cubed together rather than separately) inside of a cubic root, they cancel each other out.

So this simplifies to h(f(x)) = 2 *( 3x - 5) + 8 Now we distribute the 2 (PEMDAS)

h(f(x)) = 6x - 10 + 8 Now we combine like terms!

h(f(x)) = 6x - 2

And that's the answer! I see that this is the second question like this you have posted today, please feel free to reach out to me if you would like extra help this year with your algebra work. I hope this helps! :)

Answer 2

When you have a function like f(x), the value you place in the parenthesis defines the value 'x'. For example:

f(x) = x+1

f(1) = 1+1 = 2

f(2) = 2+1 = 2

f(pig) = pig + 1

Knowing this, we can write out the expression h(f(x))

h(x) = 23√x +8

Substitute the 'x' in this equation with the value of f(x) given in the problem statement.

h(f(x)) = 23√((3x-5)^3) +8