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# Function Composition

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Let \$f(x) = 2x - 3\$ and \$g(f(x)) = 5-4x.\$. Find \$g(4)\$.

May 4, 2021

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We see \$f(x)\$ appears inside of \$g(x)\$, which is \$g(f(x))\$

Therefore we can conclude that

\$g(2x-3)=5-4(2x-3)\$

since we plug in the input of the \$g(x)\$ function

now we solve the \$2x-3=4\$, so we get \$2x=7, x=7/2\$ then we plug in 7/2 into the \$5-4(2x-3)\$ expression,

this gives \$5-4(7-3) = 5-4(4) = 4-16 = -12\$

I get \$\boxed{-12}\$, however I suggest you check my work as I might have misunderstood, but this should give you an idea.

May 4, 2021
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