If (f(x) = a\cos(bx + c) + d,) then range of (f(x)) is | MATH - FUNCTIONS | SolveeIt

If $f(x) = a\cos(bx + c) + d,$ then range of $f(x)$ is

$\lbrack d + a,d + 2a\rbrack$

$\lbrack a - d,a + d\rbrack$

$\lbrack d + a,a - d\rbrack$

$\lbrack d - a,d + a\rbrack$

Answer

$\lbrack d - a,d + a\rbrack$

Explanation

$f(x) = a\cos(bx + c) + d$ ….. (i)

For minimum $\cos(bx + c) = - 1$

from (i), $f(x) = - a + d = (d - a)$ ,

for maximum $\cos(bx + c) = 1$

from (i), $f(x) = a + d = (d + a)$

∴ Range of $f(x) = \lbrack d - a,d + a\rbrack$ .

Question: If \(f(x) = a\cos(bx + c) + d,\) then range of \(f(x)\) is...