Question

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

Answer 1

Answer:

The value of (g*h) (-3)  is $=-\frac{112}{3}$

Step-by-step explanation:

If $g(x) = x+\frac{1}{x}-2$ and $h(x)=4-x$

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

First multiply g(x) with f(x)

$(x+\frac{1}{x}-2)\times (4-x)$

$Distribute\:parentheses$

$=x\cdot \:4+x\left(-x\right)+\frac{1}{x}\cdot \:4+\frac{1}{x}\left(-x\right)+\left(-2\right)\cdot \:4+\left(-2\right)\left(-x\right)$

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

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

$=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x$

simplify

$=-x^2+6x+\frac{4}{x}-9$

Now, put x= -3 in above expression

$=-(-3)^2+6(-3)+\frac{4}{-3}-9$

$=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)$

$=\left(-\frac{16}{3}\right)\left(4+3\right)$

$=7\left(-\frac{16}{3}\right)$

$=-\frac{16}{3}\cdot \:7$

$=-\frac{112}{3}$

Therefore, the value of (g*h) (-3) is $-\frac{112}{3}$