Question

If f( x+1/x) = x² + 1/x² - 5, then the value of f(2) - 2f(-3) is

Answer 1

⭐⭐Answer⭐⭐

Given function is :-

$f(x+\frac{1}{x} )=x^2+\frac{1}{x^2} -5$

$=x^2+\frac{1}{x^2} +2\frac{x}{x} -7$

$=(x+\frac{1}{x})^2-7$

Now, if we consider $x+\frac{1}{x}$  as 't', then the function can be re-written as :-

$f(t)= t^2-7$

So, by substituting t as 2 and -3, we get:-

$f(2)=4-7=-3$

$2f(-3)=2(9-7)=2(2)=4$

The required question is $f(2)-2f(-3)$.

So, your final answer will be -3-4 = -7