Question

question 3
given that ( f(x) = -8x - 5 ) and ( g(x) = -3x^2 + 7x + 25 ), calculate
(a) ( f(g(-10)) = )
(b) ( g(f(10)) =
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Explanation:

Part (a)

Step1: Calculate \( g(-10) \)

Substitute \( x = -10 \) into \( g(x) = -3x^2 + 7x + 25 \):
\( g(-10) = -3(-10)^2 + 7(-10) + 25 \)
\( = -3(100) - 70 + 25 \)
\( = -300 - 70 + 25 \)
\( = -345 \)

Step2: Calculate \( f(g(-10)) \)

Substitute \( g(-10) = -345 \) into \( f(x) = -8x - 5 \):
\( f(-345) = -8(-345) - 5 \)
\( = 2760 - 5 \)
\( = 2755 \)

Part (b)

Step1: Calculate \( f(10) \)

Substitute \( x = 10 \) into \( f(x) = -8x - 5 \):
\( f(10) = -8(10) - 5 \)
\( = -80 - 5 \)
\( = -85 \)

Step2: Calculate \( g(f(10)) \)

Substitute \( f(10) = -85 \) into \( g(x) = -3x^2 + 7x + 25 \):
\( g(-85) = -3(-85)^2 + 7(-85) + 25 \)
\( = -3(7225) - 595 + 25 \)
\( = -21675 - 595 + 25 \)
\( = -22245 \)

Answer:

(a) \( \boldsymbol{2755} \)
(b) \( \boldsymbol{-22245} \)