Question

Given that f(x) = 5x − 10 and g(x) = x + 3, solve for f(g(x)) when x = −1.

Answer 1

f(x) = 5x − 10 and g(x) = x + 3

f(g(x))  = 5(x + 3) − 10
f(g(x))  = 5x + 15 − 10
f(g(x))  = 5x + 5

when x = -1
f(g(-1))  = 5(-1) + 5
f(g(-1))  = - 5 + 5
f(g(-1))  = 0

Answer
0

Answer 2

Hi there!
The answer: f(g(x)) for x = -1 gives 0

Step I: find f(g(x)) 
f(x) = 5x − 10 and g(x) = x + 3
To find f(g(x)), we must substitute the function g(x) = x + 3 into the other equation. In other words: all the variables (x) in the function f(x) will be replaced by the function g(x)

f(g(x)) = 5(x + 3) − 10
We can now work out the parenthesis, but it isn't strictly necessary (which I'll show you later).
Parenthesis can for instance be worked out by using rainbow method.

f(g(x)) = 5x + 15 - 10
Collect the terms (by subtracting 10 from 15)

f(g(x)) = 5x + 5

Step II: find f(g(x)) when x = -1
1st option
To find the value of f(g(x)), we must substitute x = -1 into the equation. All the variables x must be replaced by -1

f(g(-1)) = 5 * -1 + 5
Multiply first.

f(g(-1)) = -5 + 5
Finally add.

f(g(-1)) = 0
Therefore the answer is 0.

2nd option
We could also use the function without working out the parenthesis, which would have given the same answer:
f(g(x)) = 5(x + 3) − 10
Substitute x = -1

f(g(-1)) = 5(-1 + 3) − 10 
Between parenthesis first!

f(g(-1)) = 5*2 − 10 
Multiply

f(g(-1)) = 10 − 10
And again, finally subtract

f(g(-1)) = 0

The answer: f(g(x)) for x = -1 gives 0
Hope this helps you!