Calculus 1 confusing me

Question

Fill in the blank with "all", "no", or "some" to make the following statements true.

Note: if answer is "all", explain why.

if your answer is "no", give an example and explain

if your answer is "some", give two examples that demonsrate when the statement is true and when it is false. explain.

(a) For real numbers x, (x + 2)^4 = x^4 + 16.

(b) For real numbers x, sqrt(x^4 + 8x^2 + 16) = x^2 + 4.

(c) For real numbers x, if (x + 2)(x − 3) = 2, then x + 2 = 2 and x − 3 = 2.

(d) For functions f and g, if f and g are both even functions, then f + g is even.

(e) For values of k, x, and y, if x < y, then kx < ky where k is a constant.

Answer 1

Hi Shahad,

Just wanted to explain Keith's answer to part B if you did not understand it. He is saying that by squaring both sides of the equation, you can prove it is true. That is, the left side has a square root function so it does not need to be squared, but when you square the other side, the equations will match up. Alternatively, you can just show that the square root of x⁴+8x²+16 is x²+4. Hope this helps!

Best,

Harsh

Answer 2