Respuesta :
Answer:
The value of (g*h) (-3) is [tex]=-\frac{112}{3}[/tex]
Step-by-step explanation:
If [tex]g(x) = x+\frac{1}{x}-2[/tex] and [tex]h(x)=4-x[/tex]
We have to find (g*h) (-3)
First multiply g(x) with f(x)
[tex] (x+\frac{1}{x}-2)\times (4-x)[/tex]
[tex]Distribute\:parentheses[/tex]
[tex]=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)[/tex]
[tex]\mathrm{Apply\:minus-plus\:rules}[/tex]
[tex]+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab[/tex]
[tex]=4x-xx+4\cdot \frac{1}{x}-\frac{1}{x}x-2\cdot \:4+2x[/tex]
simplify
[tex]=-x^2+6x+\frac{4}{x}-9[/tex]
Now, put x= -3 in above expression
[tex]=-(-3)^2+6(-3)+\frac{4}{-3}-9[/tex]
[tex]=\left(-\frac{1}{3}-3-2\right)\left(4+3\right)[/tex]
[tex]=\left(-\frac{16}{3}\right)\left(4+3\right)[/tex]
[tex]=7\left(-\frac{16}{3}\right)[/tex]
[tex]=-\frac{16}{3}\cdot \:7[/tex]
[tex]=-\frac{112}{3}[/tex]
Therefore, the value of (g*h) (-3) is [tex]-\frac{112}{3}[/tex]
