Question

PLEASE HELP

Let f(x) = 4x + 3 and g(x) = -2x + 5. Find.(f.g)(5)
a. 23
b. -17
c. -41
d. -5

Answer 1

After solving we get (f.g)(5)=-115

But the correct option is not given in the question.

Explanation:

We are given:

`f(x) = 4x+3\\g(x)=-2x+5`

We need to find (f.g)(5)

First we will multiply f and g to find (f.g) i.e

`(f.g)(x)= f(x) * g(x)\\(f.g)(x) = (4x + 3)(-2x + 5)\\(f.g)(x)=4x(-2x+5)+3(-2x+5)\\(f.g)(x)=-8x^2+20x-6x+15\\(f.g)(x)=-8x^2+14x+15\\`

Now putting x=5

`(f.g)(x)=-8x^2+14x+15\\Put \ x=5\\(f.g)(5)=-8(5)^2+14(5)+15\\(f.g)(5)=-8(25)+70+15\\(f.g)(5)=-200+70+15\\(f.g)(5)=-115`

So, after solving we get (f.g)(5)=-115

But the correct option is not given in the question.