Relations and F...

Determine all ordered pairs that satisfy $$(x - y)^{2} + x^{2} = 25$$, where $$x$$ and $$y$$ are integers and $$x \geq 0$$. Find the number of different values of $$y$$ that occur

Express $$\dfrac {b}{a^{5}} $$ in terms of $$t$$ given that $$a = \sqrt [3]{t}$$ and $$b = t^{2}$$.

If $$f(x) = x^{2} - x$$ and $$g(x) = 3x + 2$$, what is $$g(f(1)) - 2$$?

$$f(x)=x-\dfrac{1}{x}$$, then $$f(\dfrac{1}{x})=$$
I. $$f(x)$$
II. $$f(-x)$$
III. $$-f(x)$$
IV. $$\dfrac{1}{f(x)}$$

If $$f(x) = 3x + 5$$ and $$f(g(x)) = 6x - 4$$, what is $$g(x)$$?

What positive value(s) of x, less than $$360^o$$, will give a minimum value for 4 - 2 sin x cos x?

If $$f(x)=\dfrac{x+1}{x-1}$$, what is the value of $$f(f(f(f((\frac{3}{5}))))$$?

In the problem below, $$f(x)={x}^{2}$$ and $$g(x)=4x-2$$
Find the following function: $$(f+g)(x)$$

If $$p - q > 0$$, which of the following is true?

If $$f(x) = 3x - 2$$ and $$g(x) = 7, f[g(x)] =$$