# (fog) (-1) f(x) =3xsquared -1 g(x)=2x +7

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We can solve this problem by first plugging-in -1 for x in g(x).

`g(-1)=2(-1)+7=-2+7=5 `

So, we will have:

`(f o g)(-1) = f(g(-1)) `

`=f(5) `

`= 3(5)^2 - 1`

`=3(25) - 1 `

`= 75 - 1 `

`= 74`

Therefore, `(f o g)(-1) = 74. `

Given: `f(x) =3x^2 -1 ` and `g(x)=2x+7`

To find fog(x), compute f(g(x)) first.

Substitute the function of g i.e here, 2x+7 for g(x) in the composition to get:

f(2x+7)

Now, substitute this expression (2x+7) into function f in the place of x-value.

Thus, `fog(x)=3*(2x+7)^2-1`

`=3(4x^2+28x+49)-1`

`=12x^2+84x+147-1`

`=12x^2+84x+146`

Substitute the value of x, to get

`fog(-1)=12(-1)^2+84(-1)+146`

=12-84+146

**=74**

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The value of (fog)(-1) is to be determined given that f(x) = 3x^2 -1 and g(x)=2x +7

fog(-1) is the same as f(g(-1))

First determine g(-1)

Substitute x = -1 in g(x) = 2x + 7

g(-1) = 2*-1 + 7 = 7 - 2 = 5

Now f(5) = 3*5^2 - 1

= 3*25 - 1

= 75 - 1

= 74

The required value of gof(-1) = 74