if f(x)=4x and g(x)=5x+1, then what is the rule for f(2g(x))? what is the rule for g(f(x)+1)?

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if f(x)=4x and g(x)=5x+1, then what is the rule for f(2g(x))? what is the rule for g(f(x)+1)?

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    2021-09-08T21:20:11+00:00

    Given

    • f(x)=4x;
    • g(x)=5x+1.

    1. Find the rule for f(2g(x)):

    f(2g(x))=f(2\cdot (5x+1))=f(10x+2)=4\cdot (10x+2)=40x+8.

    2. Find the rule for g(f(x)+1):

    g(f(x)+1)=g(4x+1)=5\cdot (4x+1)+1=20x+5+1=20x+6.

    Answer: f(2g(x))=40x+8, g(f(x)+1)=20x+6.

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