Question

F(x) = 3 x + 1 and g (x) = 2x - 3. find f (g(x)) and g (f(x))

Answer 1

Explanation:

f(g(x)) means substituting g(x) in f(x)

ie, 3(2x-3)+1 = 6x-9+1 = 6x - 8

g(f(x)) means substituting f(x) in g(x)

ie, 2(3x+1)-3 = 6x2-3 = 6x - 1

Answer 2

Explanation:

f(x} = 3x + 1

g(x} = 2x -- 3

f(g(x)) = 3x + 1. (Calm down right?)

Let the x in the expression be (2x -- 3)

N.B x = g{x}

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

Open bracket

f(g(x)) = 6x -- 9 + 1

f(g(x)) = 6x -- 8...

2... Solve for g(f(x)), using the same strategy

g(f(x)) = 2x -- 3

x = f(x)

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

g(f(x)) = 6x + 2 -- 3

g(f(x)) = 6x -- 1

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