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f(x) = 3x + a & g(x) = b-5x
Given that gf(1) = 2 and g-1(7) = 1, find the value of “a” and the value of “b”


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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}f(x)&=&3x+a\\g(x)&=&b-5x\\g(f(1))&=&2\\g^{-1}(7)&=&1\\\end{array}\right.\\\\\\g(f(x))=g(3x+a)=b-5(3x+a))=b-15x-5a\\g(f((1))=b-15-5a=2\\\\\\g(x)=y=b-5x\\x=b-5y\\5y=b-x\\y=\dfrac{b-x}{5} \\g^{-1}(x)=\dfrac{b-x}{5} g^{-1}(7)=\dfrac{b-7}{5} =1\\b-7=5\\\\\boxed{b=12}\\\\\left\{\begin{array}{ccc}b&=&12\\5a-b&=&-17\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b&=&12\\5a-12&=&-17\\\end{array}\right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}a&=&-1\\b&=&12\\\end{array}\right.\\\\\\[/tex]

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