Question

Let $f(x)$={-$5,x≤0 x-5,x>0$ and $g(x)=If(x)+2f(IxI)$.Then $g(-2)$ will be

• A. $-15$
• B. $1$
• C. $0$
• D. $1$
• E. $-11$

Answer 1

Answer: (E)

$-11$

Answer 2

Given that

$f(x)$={$−5,x−5,​x≤0x>0​$

$g(x)=f(x)+2f(∣x∣)$

now $g(−2)$ can be found by

Step 1: Since 2≤0, we use the first part of the definition of $f(x),$ which gives us $f(−2)=−5$.

Step 2: Since $∣−2∣=2$ and $2>0,$ we use the second part of the definition of f(x), which gives us $f(∣−2∣)=∣2∣−5=2−5=−3$.

Step 3: Using the formula $g(x)=f(x)+2f(∣x∣)$, we have:$g(−2)=f(−2)+2f(∣−2∣)=(−5)+2(−3)=−5−6=−11.$

Therefore, the value of $g(−2)\text{is } -11$. (_Ans.)