Question

If $f\left(x\right)=a{x}^7+b{x}^3+cx-5a,b,c$ are real constants and $f(-7)=7$ then the range of $f\left(7\right)+17\cos x$ is

• A. $\left[-34,0\right]$
• B. $\left[0,34\right]$
• C. $\left[-34,34\right]$
• D. $\left[34,\infty \right]$

Answer 1

The correct option is A $\left[-34,0\right]$

$f\left(x\right)=a{x}^7+6x^3+cx-5$

$f(-7)=7$

$f\left(7\right)+f(-7)=-10$

$f\left(7\right)+7=-10$

$f\left(7\right)=-17$

Range of $-17+17\cos x$ is form $[-34,0]$