f ( x ) = 7 x + 2 and g ( x ) = − 2x squared − x − 15, calculate (please show me step by step.

Question

f (g(1)) =

g(f(3))=

Answer 1

f(x) = 7x + 2

g(x) = -2x² - x - 15

f(g(1)) = f(-2(1)² - (1) - 15)

= f(-2(1) - 1 - 15)

= f(-2 - 1 - 15)

= f(-18)

= 7(-18) + 2 = -126 + 2 = -124

g(f(3)) = g(7(3) + 2)

= g(21 + 2)

= g(23)

= -2(23)² - (23) - 15 = -2(529) - 23 - 15 = -1058 - 23 - 15 = -1096

Answer 2

Hi Devin. First you want to solve for g(1) by substituting 1 for each x in that equation:

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

g(1) = -2 (1)^2 - 1 - 15

g(1) = -2 -1 -15

g(1) = -18

Next, substitute your answer for g(1), -18, into each x in the f(x) = 7x + 2 equation:

f(x) = 7x + 2

f(g(1)) = 7(-18) + 2

f(g(1)) = -126 + 2

f(g(1)) = -124

For the next problem first solve for f(3) by substituting 3 for each x in that equation:

f(x) = 7x + 2

f(3) = 7(3) + 2

f(3) = 21 + 2

f(3) = 23

Next, substitute your answer for f(3), 23, for each x in the g(x) equation:

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

g(f(3)) = -2(23)^2 - 23 - 15

g(f(3)) = -1058 - 23 - 15

g(f(3)) = -1096

I hope this helps!