Math

QuestionEvaluate the function g(x)=3x25g(x)=3 x^{2}-5 at the following: (a) g(4)g(-4), (b) g(b)g(b), (c) g(x3)g(x^{3}), (d) g(3x4)g(3 x-4).

Studdy Solution

STEP 1

Assumptions1. The function is defined as g(x)=3x5g(x)=3 x^{}-5 . We are asked to evaluate the function at different values of xx

STEP 2

To evaluate the function g(x)g(x) at a particular value, we substitute that value in place of xx in the function.
(a) For g(4)g(-4), we substitute xx with 4-4 in the function g(x)g(x).
g(4)=(4)25g(-4) =(-4)^{2}-5

STEP 3

Calculate the value of g()g(-).
g()=3()25=3(16)5=485=43g(-) =3(-)^{2}-5 =3(16)-5 =48-5 =43So, g()=43g(-)=43.

STEP 4

(b) For g(b)g(b), we substitute xx with bb in the function g(x)g(x).
g(b)=3b2g(b) =3b^{2}-So, g(b)=3b2g(b)=3b^{2}-.

STEP 5

(c) For g(x3)g\left(x^{3}\right), we substitute xx with x3x^{3} in the function g(x)g(x).
g(x3)=3(x3)25g\left(x^{3}\right) =3(x^{3})^{2}-5

STEP 6

implify the expression g(x3)g\left(x^{3}\right).
g(x3)=3(x6)5=3x65g\left(x^{3}\right) =3(x^{6})-5 =3x^{6}-5So, g(x3)=3x65g\left(x^{3}\right)=3x^{6}-5.

STEP 7

(d) For g(3x4)g(3 x-4), we substitute xx with (3x4)(3x-4) in the function g(x)g(x).
g(3x4)=3(3x4)25g(3x-4) =3(3x-4)^{2}-5

STEP 8

Expand and simplify the expression g(3x4)g(3x-4).
g(3x4)=3(x224x+16)5=27x272x+485=27x272x+43g(3x-4) =3(x^{2}-24x+16)-5 =27x^{2}-72x+48-5 =27x^{2}-72x+43So, g(3x4)=27x272x+43g(3x-4)=27x^{2}-72x+43.

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