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Julli [10]
3 years ago
13

For all values of x, f(x) = 2x-3 and g(x) = x^2 + 1 a) Find fg(x) Simplify and give your answer in the form ax^2 + b b) Find gf(

x).
Mathematics
1 answer:
Inessa [10]3 years ago
6 0

Answer:

fg(x) = 2x² - 1

gf(x) = 4x²-12x +10

Step-by-step explanation:

Given the functions f(x) = 2x-3 and g(x) = x^2 + 1

a) f(g(x)) = f(x²+1)

f(x²+1) = 2(x²+1) -3

f(x²+1)= 2x²+2 -3

f(x²+1) = 2x² - 1

fg(x) = 2x² - 1

Hence function fg(x) is 2x² - 1

b) gf(x) = g(2x-3)

g(2x-3) = (2x-3)² + 1

g(2x-3) = (2x-3)(2x-3) + 1

g(2x-3) = 4x²-6x-6x+9 + 1

g(2x-3) = 4x²-12x +10

gf(x) = 4x²-12x +10

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First start with the left side, doing distributive property

So... -2(x) = -2x and -2(5) = -10 Therefore on the left side you now have -2x -10

Next do the same on the right side

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Now that you have simplified both sides the problem now looks like this:

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Because you have equal terms on both sides (-2) those cancel out so you have -10 = 9

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