If f(x) = a (bx + c) + d, then range of f(x) is - Vidyadip

MCQ

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

A
$[d + a,\;d + 2a]$
B
$[a - d,\;a + d]$
C
$[d + a,\;a - d]$
✓
$[d - a,\;d + a]$

✓

Answer

Correct option: D.

$[d - a,\;d + a]$

d
(d) $f(x) = a\cos (bx + c) + d…..(i)$

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

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

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

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

$\therefore$ Range of $f(x) = [d - a,\,\,d + a]$

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