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8090 [49]
3 years ago
15

F(x)=

Mathematics
1 answer:
lana66690 [7]3 years ago
8 0

Answer:

(g\ o\ f)(x) = -10x^2 + 25x + 44

Step-by-step explanation:

Given

f(x) = 2x^2 - 5x - 8

g(x) = -5x+4

Required

Find:\ (g\ o\ f)(x)

In functions;

(g\ o\ f)(x) = g(f(x))

Substitute f(x) = 2x^2 - 5x - 8 in (g\ o\ f)(x) = g(f(x))

(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))

Solving for g(f(2x^2 - 5x - 8))

If g(x) = -5x+4

then

g(f(2x^2 - 5x - 8)) = -5(2x^2 - 5x - 8) + 4

Open Bracket

g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 40 + 4

g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 44

Recall that:

(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))

This implies that

(g\ o\ f)(x) = -10x^2 + 25x + 44

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