Question

If g(x)*x+1/x-2 abd h(x)=4-x, what is the value of (g*h) (-3)

Answer 1

The value of (g*h) (-3) is
`=-(112)/(3)`

Step-by-step explanation:

If
`g(x) = x+(1)/(x)-2` and
`h(x)=4-x`

We have to find (g*h) (-3)

First multiply g(x) with f(x)

`(x+(1)/(x)-2)* (4-x)`

`Distribute\:parentheses`

`=x\cdot \:4+x\left(-x\right)+(1)/(x)\cdot \:4+(1)/(x)\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)`

`\mathrm{Apply\:minus-plus\:rules}`

`+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab`

`=4x-xx+4\cdot (1)/(x)-(1)/(x)x-2\cdot \:4+2x`

simplify

`=-x^2+6x+(4)/(x)-9`

Now, put x= -3 in above expression

`=-(-3)^2+6(-3)+(4)/(-3)-9`

`=\left(-(1)/(3)-3-2\right)\left(4+3\right)`

`=\left(-(16)/(3)\right)\left(4+3\right)`

`=7\left(-(16)/(3)\right)`

`=-(16)/(3)\cdot \:7`

`=-(112)/(3)`

Therefore, the value of (g*h) (-3) is
`-(112)/(3)`