91Ó°ÊÓ

Evaluate the indicated expression assuming that \(f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1|\). $$ (f \circ g)(5) $$

Assume \(f(x)=\frac{x+2}{x^{2}+1}\) for every real number \(x .\) Evaluate and simplify each of the following expressions. \(f(3 a-1)\)

Check your answer by evaluating the appropriate function at your answer. Suppose \(h(t)=\frac{2-3 t}{4+5 t}\). Find a formula for \(h^{-1}\).

Suppose \(f(x)=2+\frac{x-5}{x+6}\). (a) Evaluate \(f^{-1}(4)\). (b) Evaluate \((f(4))^{-1}\). (c) Evaluate \(f\left(4^{-1}\right)\).

Sketch a coordinate plane showing the following four points, their coordinates, and the rectangles determined by each point (as in Example 1): \((1,2),(-2,2),(-3,-1),\) (2,-3)

Evaluate the indicated expression assuming that \(f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1|\). $$ (g \circ f)(4) $$

Assume \(f(x)=\frac{x+2}{x^{2}+1}\) for every real number \(x .\) Evaluate and simplify each of the following expressions. \(f\left(x^{2}+1\right)\)

Evaluate the indicated expression assuming that \(f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1|\). $$ (g \circ f)(5) $$

Assume \(f(x)=\frac{x+2}{x^{2}+1}\) for every real number \(x .\) Evaluate and simplify each of the following expressions. \(f\left(2 x^{2}+3\right)\)

Sketch a coordinate plane showing the following four points, their coordinates, and the rectangles determined by each point (as in Example 1 ): (2.5,1),(-1,3) , (-1.5,-1.5),(1,-3)