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Let [tex]f(x) = 2x + 8[/tex], [tex]g(x) = x^2 + 2x - 8[/tex], and [tex]h(x) = 3x - 6[/tex].

Perform the indicated operation and simplify as far as possible:

[tex](g - f)(2) = \square[/tex]

Sagot :

GinnyAnsweridn
To solve [tex]\((g - f)(2)\)[/tex], we need to break down the problem step by step.

1. Identify the given functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ f(x) = 2x + 8 \][/tex]
[tex]\[ g(x) = x^2 + 2x - 8 \][/tex]

2. Determine [tex]\( g(x) - f(x) \)[/tex]:
[tex]\[ g(x) - f(x) = (x^2 + 2x - 8) - (2x + 8) \][/tex]
Simplify the expression by distributing and combining like terms:
[tex]\[ g(x) - f(x) = x^2 + 2x - 8 - 2x - 8 \][/tex]
[tex]\[ g(x) - f(x) = x^2 - 16 \][/tex]

3. Evaluate the simplified expression at [tex]\( x = 2 \)[/tex]:
[tex]\[ (g - f)(2) = 2^2 - 16 \][/tex]
[tex]\[ (g - f)(2) = 4 - 16 \][/tex]
[tex]\[ (g - f)(2) = -12 \][/tex]

Thus, the result of the operation [tex]\( (g - f)(2) \)[/tex] is:
[tex]\[ (g-f)(2) = -12 \][/tex]
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