Question

Can someone check if this is right or did I solve it wrong?

The function y = f (x) is linear. Given f-¹ (0) = 3 and f (1) = - 4, find the formula f (x) and f-¹ (x).

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Answer 1

f(3x) - 2g(x+1) = 12x - 5

Explanation:

You've got f[g(x)] and g[f(x)] correct

However, f(3x) means substitute 3x for x in f(x):

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

⇒ f(3x) = 6x - 3

2g(x+1) = 2[4 - 3(x + 1)]

⇒ 2g(x+1) = 2[4 - 3x -3]

⇒ 2g(x+1) = 2[1 - 3x]

⇒ 2g(x+1) = 2 - 6x

f(3x) - 2g(x+1) = (6x - 3) - (2 - 6x)

⇒ f(3x) - 2g(x+1) = 12x - 5