Question

Let f(x) = - 3x – 1 and g(x) = x^2 – 3.

Find (fog)(-1).
Then (fog)( - 1)= (Simplify your answer.)

Answer 1

Given:

f(x) = 5x² - x + 1

g(x) = -3x

Let's determine (f o g)(1),

(f o g)(1) = f(g(1))

Step 1: Let's determine g(1).

`\text{ }g\mleft(x\mright)=-3x`
`g\mleft(1\mright)=-3(1)\text{ = -3}`

Step 2: Substitute g(1) as x in f(x).

`f\mleft(x\mright)=5x^2-x+1`
`\mleft(f\circ g\mright)\mleft(1\mright)=f\mleft(g\mleft(1\mright)\mright)=5(-3)^2\text{ - (-3) + 1}`
`=5(9)\text{ + 3 + 1}`
`=45\text{ + 4}`
`\text{ }(f\circ g)(1)=\text{ 49}`

Therefore, the answer is letter A. (f o g)(1) = 49