Explain why the function y=1-cosx is an even function

Mathematics

1 answer:

Oksanka [162]2 years ago

8 0

A function is said to even if it returns the same output when given two opposite inputs:

$f(x) = f(-x)$

In your case, you have

$f(x) = 1-\cos(x), \quad f(-x) = 1-\cos(-x)$

And since $\cos(x) = \cos(-x)$ , the proof is concluded.

You might be interested in

Matilda, Tanya and Renee are auditioning for a play. In how many ways can the girls fill the roles of a grandmother, mother, and

solmaris [256]

The girls fill the roles of a grandmother, mother, and daughter by permutation. It is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged. Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

5 0

3 years ago

Read 2 more answers

H(x)=1/8x^3-x^2<br><br> Over which interval does h have a positive average rate of change?

lara31 [8.8K]

Answer:

$(-\infty,0)\cup(\frac{16}{3},\infty)\\That \ is x\frac{16}{3}$

Step-by-step explanation:

$h(x)=\frac{1}{8}x^{3} -x^{2} \\\\Differentiate \ h(x) \ with \ respect \ to \ x\\h'(x)=\frac{3}{8}x^{2} -2x$

For positive rate of change $h'(x)>0$

$\frac{3}{8} x^{2} -2x>0\\x(\frac{3}{8}x-2)>0\\\\ When \ x0 \ (multiplication \ of \ two \ positives \ is \ positive)\\\\h'(x)>0 \ when \ x\frac{16}{3} \\\\$