Question

Find the range of the function
f(x) =(4sin^2x + 3)/7



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Answer 1

Step-by-step explanation:

We have,

$f(x) = \frac{4 \sin^{2} (x) + 3}{7}$

We know that,

$0 \leqslant \sin^{2} (x) \leqslant 1$

$\implies0 \leqslant 4 \sin^{2} (x) \leqslant 4$

$\implies3 \leqslant 4 \sin^{2} (x) + 3 \leqslant 7$

$\implies \frac{3}{7} \leqslant \frac{4 \sin^{2} (x) + 3 }{7} \leqslant \frac{7}{7}$

$\implies \frac{3}{7} \leqslant f(x) \leqslant 1$

Hence, the range of f(x) is [ 3/7 , 1 ]