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Standard XII

Mathematics

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Question

Suppose that the function $f$ is defined for all real numbers $r$ by the formula $f (r) = 2 (r - 1) + 3$ . Evaluate $f$ at the input values $0, 2, x + 2$ , and $f (2)$ .

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Solution

In each case, we substitute the given input value for $r$ into the formula for $f$ :
$f (0) = 2 (0 - 1) + 3 = - 2 + 3 = 1$
$f (2) = 2 (2 - 1) + 2 = 2 + 3 = 5$
$f (x + 2) = 2 (x + 2 - 1) + 3 = 2 x + 5$
$f (f (2)) = f (5) = 2 (5 - 1) + 3 = 11$ .

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Suppose that the function f is defined for all real numbers r by the formula f(r)=2(r−1)+3. Evaluate f at the input values 0,2,x+2, and f(2).

In each case, we substitute the given input value for r into the formula for f:f(0)=2(0−1)+3=−2+3=1f(2)=2(2−1)+2=2+3=5f(x+2)=2(x+2−1)+3=2x+5f(f(2))=f(5)=2(5−1)+3=11.

Suppose that the function $f$ is defined for all real numbers $r$ by the formula $f (r) = 2 (r - 1) + 3$ . Evaluate $f$ at the input values $0, 2, x + 2$ , and $f (2)$ .

In each case, we substitute the given input value for $r$ into the formula for $f$ :
$f (0) = 2 (0 - 1) + 3 = - 2 + 3 = 1$
$f (2) = 2 (2 - 1) + 2 = 2 + 3 = 5$
$f (x + 2) = 2 (x + 2 - 1) + 3 = 2 x + 5$
$f (f (2)) = f (5) = 2 (5 - 1) + 3 = 11$ .