Output Is Input

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evaluating

Graphs

Let $T$ be a function. Its graph is shown here.

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Using the graph estimate the following values.

$T(2) = \answer [tolerance=0.1]{-5.9}$
$T(-6) = \answer [tolerance=0.1]{3.95}$
$T(0) = \answer [tolerance=0.1]{3}$

Let $f$ be a function. Its graph is shown here.

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All of the values of $T$ you determined above were real numbers.

$T(2)$ is a real number.
$T(-6)$ is a real number.
$T(0)$ is a real number.

Therefore, we could evaluate $f$ at these numbers.

Using the graph estimate the following values.

$f(T(2)) = \answer [tolerance=0.1]{3}$
$f(T(-6)) = \answer [tolerance=0.1]{4}$
$f(T(0)) = \answer [tolerance=0.1]{2.75}$

Use the graphs above to approximate the following expressions.

(a): $f(T(8)) = \answer [tolerance=0.1]{2.37}$
(b): $T(f(0)) = \answer [tolerance=0.1]{-1.089}$
(c): $f(f(-4)) = \answer [tolerance=0.1]{0.9}$
(d): $T(T(3)) = \answer [tolerance=0.1]{3.036}$
(e): $f(T(-2.5)) = \answer [tolerance=0.1]{0.874}$
(f): $T(f(-1))+1 = \answer [tolerance=0.1]{-6.058}$
(g): $f(f(-6)) -5 = \answer [tolerance=0.1]{-2.255}$

Formulas

Define the functions $M$ , $N$ , and $P$ by the following formulas with their implied or natural domains.

$\blacktriangleright$ $M(t) = t^2 - 1$

$\blacktriangleright$ $N(k) = \frac {k^2}{k + 1}$

$\blacktriangleright$ $P(\theta ) = 3 \, \cos (\theta ) + 2$

Use the formulas above to approximate the following expressions.

(a): $N(M(1.7)) = \answer [tolerance=0.1]{1.236}$
(b): $M(P(0)) = \answer [tolerance=0.1]{24}$
(c): $N(N(8.3)) = \answer [tolerance=0.1]{6.526}$
(d): $P(P(-\pi )) = \answer [tolerance=0.1]{3.621}$
(e): $M(N(-2.5)) = \answer [tolerance=0.1]{16.361}$
(f): $N(M(-2.5)) = \answer [tolerance=0.1]{4.41}$

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more examples can be found by following this link
More Examples of Pointwise Composition