Question

Find goh g(x)=5x and h(x)=x^2+x-1 ?

Answer 1

`5(x^2+x-1)`

Explanation:

I think it is often useful to "describe" with words what functions do to solve problems like this. You can think that, whenever you give some number to the function `h`, it returns that number squared, plus the number itself, minus one.
On the other hand, the function `g` simply returns five times whatever you gave it in the first place.

Composing two functions means giving the output of the inner function as input to the outer function. The workflow would be like this:

• Take any number `x`
• Give that number to the function `h`, and collect the output `h(x)`
• Give that output as input to the function `g`, and compute `g(h(x))` as the final output.

So, after the first two steps, we gave a number `x` to the function `h`, and we have `h(x) = x^2+x-1`. Then, we give this number to `g`. But what does `g` do? Simply return whatever it receives, five times. Since it received `x^2+x-1`, it will return `5(x^2+x-1)`