Question

ゆうや

一枚目が問題で二番目が答えなんですがわかる方教えください。

EVALUATING FUNCTIONS
The symbol f(x) represents the real number in the range of the function
f corresponding to the domain value x. Symbolically, f:x →S(x). The ordered
pair (x, (x)) belongs to the function f. If xisa real number that is not in the
domain of f, then fis not defined at x and f(x) does not exist.
Examples:
15
a)
Find f(6), f(a), and f(6+a) for f(x)
X -
3°
b)
Find g(7), g(h), and g(7+h) for g(x)
= 16+ 3x
x.
2
c)
Find k(9), 4k(a), and k(4a) for k(x) =
2
For the above functions, determine the resulting domain.
Solutions:
a)
b)
c)

Answers (page 5)
15
S(x)=
X-3
Rational function
a
f(6) = 15 /6 -3= 15 /3= 5
f(a) = 15 / a - 3
f(6+a) = 15 / 6+a-3= 15/a+3
Restriction: The denominator cannot be equals to 0
x-3+0
X+3
Domain: {xe RIx + 3}
b g(x)=16+3x-x Quadratic function
g(7)=16+3(7) -7?=-12
g(h)=16+3h-h?
g(7+h)=16+3(7+h)-(7+h)°
=16+21+
6-(49+14h+h°)
= 37 + 3h-49-14h-h°
=-° -11h-12
(7+h)(7+h)=49+ 7h+7h+h°
= 49+14h+ h?
Domain: {xe R}