Question 174507
Find f(g(x)) given f(x)= x - 10 , g(x)= -2x^2 - 5

You know what g(x) is, right?

g(x) = -2x^2 - 5

You want to find f of g(x).

So, plug the value of g(x), which is (-2x^2 - 5) into the value for f(x), which is (x - 10) and simplify.

f(g(x)) = (-2x^2 - 5) - 10

f(g(x)) = -2x^2 - 5 - 10

f(g(x)) = -2x^2 - 15

That's it.

Understood?

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I received your e-mail.

You want to find the domain of -2x^2 - 15???

The domain will be all the values that we can safely replace x with in the given function.

The domain of the function f(g(x)) = -2x^2 - 15 is: ALL REAL NUMBERS.

You see, we can replace x with any number here without affecting anything regarding the function itself.

DOMAIN = ALL REAL NUMBERS