Question

Read the information given below and answer the question that follows. F(x) = x3 - 3 , g(x) = (1/x) - x Find the value of fog(-1) - gof(-1).

Answer 1

put the value of f(-1) we get= -1×3-3= -6 like u can solve akk

Answer 2

The correct answer is $\frac{-27}{4}$.

Given: f(x) = $x^{3}-3$ and g(x) = $\frac{1}{x}-x$.

To Find: The value of fog(-1) - gof(-1).

Solution:

fog(x) = f(g(x)) = $g(x)^{3}-3$.

fog(x) = $(\frac{1}{x}-x )^{3} -3$

Now put x = -1.

fog(-1) = $(\frac{1}{(-1)}-(-1) )^{3} -3$

fog(-1) = $(-1+1)^{3} -3$

fog(-1) = 0 - 3

fog(-1) = -3

gof(x) = $\frac{1}{f(x)}-f(x)$

gof(x) = $\frac{1}{x^{3} -3}-(x^{3} -3)$

gof(x) = $\frac{1}{x^{3} -3}-x^{3} +3$

Now put x = -1.

gof(-1) = $\frac{1}{(-1)^{3} -3}-(-1)^{3} +3$

gof(-1) = $\frac{1}{-1 -3}-(-1 )+3$

gof(-1) = $\frac{-1}{4}+4$

gof(-1) = $\frac{15}{4}$

Now put the value of fog(-1) and gof(-1) in the equation.

fog(-1) - gof(-1) = $-3-\frac{15}{4}$

fog(-1) - gof(-1) = $\frac{-12-15}{4}$

fog(-1) - gof(-1) = $\frac{-27}{4}$

Hence, the value of fog(-1) - gof(-1) is $\frac{-27}{4}$.

#SPJ2