Question

range of f(x)=acosx+bsinx+c

Answer 1

$c- \sqrt{ a^{2} + b^{2} } \leq a cos x +bsin x+c \leq c+ \sqrt{ a^{2} + b^{2} }$

Answer 2

The range of the function f(x) = acosx + bsinx + c is   $c\:\pm\:\sqrt{a^{2} -b^{2} }$

• Range of a function : The range of the function is defined as the complete set of values obtained for a variable
• The range of function is usually represented as $\{a,b\}$ where a is minimum value and b is maximum value of the function

• Minimum value of acosx + bsinx + c is   $c-\sqrt{a^{2}+b^{2}}$

• Minimum value of acosx + bsinx + c is   $c+\sqrt{a^{2}+b^{2}}$

• The range of the function is   $\{c-\sqrt{a^{2}+b^{2}}, c+\sqrt{a^{2}+b^{2}}\}$