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For functions
f(x) and
g(x),g(x)=f(x+3)-12. If
f(4)=112, what is the value of
g(1) ?

$32$ . For functions $f(x)$ and $g(x), g(x)=f(x+3)-12$ . If $f(4)=112$ , what is the value of $g(1)$ ?

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Write and solve direct variation equations

Full solution

Q.

32

. For functions

f(x)

and

g(x), g(x)=f(x+3)-12

. If

f(4)=112

, what is the value of

g(1)

?

Define $g(x)$ in terms of $f(x)$ : $g(x)$ is defined in terms of $f(x)$ , so we need to find the value of $f(x)$ when $x$ is $1 + 3$ , which is $f(4)$ .
Find $f(4)$ : We know $f(4) = 112$ from the problem.
Calculate $g(1)$ : Now we plug $f(4)$ into the equation for $g(x)$ : $g(x) = f(x+3) - 12$ . So, $g(1) = f(1+3) - 12 = f(4) - 12$ .
Calculate $g(1)$ : Now we plug $f(4)$ into the equation for $g(x)$ : $g(x) = f(x+3) - 12$ . So, $g(1) = f(1+3) - 12 = f(4) - 12$ . Substitute $f(4) = 112$ into the equation: $g(1) = 112 - 12$ .
Calculate $g(1)$ : Now we plug $f(4)$ into the equation for $g(x)$ : $g(x) = f(x+3) - 12$ . So, $g(1) = f(1+3) - 12 = f(4) - 12$ . Substitute $f(4) = 112$ into the equation: $g(1) = 112 - 12$ . Calculate $g(1)$ : $g(1) = 100$ .

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