Step-by-step explanation:
a) (f - g)(x) = (x - 3) - (x² + 2x - 15)
=>(f - g)(x) = x - 3 - x² - 2x + 15
=>(f - g)(x) = -x² + x - 2x - 3 + 15
=>(f - g)(x) = -x² - x + 12 => ANSWER
b) (f + g)(x) = (x - 3) + (x² + 2x - 15)
=>(f + g)(x) = x - 3 + x² + 2x - 15
=>(f + g)(x) = x² + x + 2x - 3 - 15
=>(f + g)(x) = x² + 3x - 18 => ANSWER
c) (f • g)(x) = (x - 3)×(x² + 2x - 15
=>(f • g)(x) = x³ + 2x² - 15x - 3x² -6x + 45
=>(f • g)(x) = x³ - x² - 21x + 45 => ANSWER
d) (g/f)(x) = x² + 2x - 15/x - 3
=>(g/f)(x) = (x + 5)(x - 3)/x - 3
=>(g/f)(x) = x + 5/1
=>(g/f)(x) = x + 5 =>ANSWER
e) (f - g)(-5) = (x - 3) - (x² + 2x - 15
=>(f - g)(-5) = (-5 - 3) - ((-5)² + 2(-5) - 15)
=>(f - g)(x) = (-8) - (25 - 10 - 15)
=>(f - g)(x) = (-8) - (0)
=>(f - g)(x) = -8 => ANSWER
f) (g ° f)(-4) = g[f(x)]
=> f(-4) = x - 3
=> f(-4) = -4 - 3
=> f(-4) = -7
=> g(-7) = x² + 2x - 15
=> g(-7) = (-7)² + 2(-7) - 15
=> g(-7) = 49 - 14 - 15
=> g(-7) = 35 - 15
=> g(-7) = 20
=> (g ° f)(-4) = 20 => ANSWER
another step for (g ° f)(-4)
=> (g ° f)(-4) = g[f(x)]
=> (g ° f)(x) = (x - 3)² + 2(x - 3) - 15
=> (g ° f)(x) = (x - 3)(x - 3) + 2x - 6 - 15
=> (g ° f)(x) = x² - 6x + 9 + 2x - 21
=> (g ° f)(x) = x² - 4x - 12
=> (g ° f)(-4) = (-4)² - 4(-4) - 12
=> (g ° f)(-4) = 16 + 16 - 12
=> (g ° f)(-4) = 32 - 12
=> (g ° f)(-4) = 20 => SAME ANSWER
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Answers & Comments
Step-by-step explanation:
f(x) = x - 3
g(x) = x² + 2x - 15
a) (f - g)(x) = (x - 3) - (x² + 2x - 15)
=>(f - g)(x) = x - 3 - x² - 2x + 15
=>(f - g)(x) = -x² + x - 2x - 3 + 15
=>(f - g)(x) = -x² - x + 12 => ANSWER
b) (f + g)(x) = (x - 3) + (x² + 2x - 15)
=>(f + g)(x) = x - 3 + x² + 2x - 15
=>(f + g)(x) = x² + x + 2x - 3 - 15
=>(f + g)(x) = x² + 3x - 18 => ANSWER
c) (f • g)(x) = (x - 3)×(x² + 2x - 15
=>(f • g)(x) = x³ + 2x² - 15x - 3x² -6x + 45
=>(f • g)(x) = x³ - x² - 21x + 45 => ANSWER
d) (g/f)(x) = x² + 2x - 15/x - 3
=>(g/f)(x) = (x + 5)(x - 3)/x - 3
=>(g/f)(x) = x + 5/1
=>(g/f)(x) = x + 5 =>ANSWER
e) (f - g)(-5) = (x - 3) - (x² + 2x - 15
=>(f - g)(-5) = (-5 - 3) - ((-5)² + 2(-5) - 15)
=>(f - g)(x) = (-8) - (25 - 10 - 15)
=>(f - g)(x) = (-8) - (0)
=>(f - g)(x) = -8 => ANSWER
f) (g ° f)(-4) = g[f(x)]
=> f(-4) = x - 3
=> f(-4) = -4 - 3
=> f(-4) = -7
=> g(-7) = x² + 2x - 15
=> g(-7) = (-7)² + 2(-7) - 15
=> g(-7) = 49 - 14 - 15
=> g(-7) = 35 - 15
=> g(-7) = 20
=> (g ° f)(-4) = 20 => ANSWER
another step for (g ° f)(-4)
=> (g ° f)(-4) = g[f(x)]
=> (g ° f)(x) = (x - 3)² + 2(x - 3) - 15
=> (g ° f)(x) = (x - 3)(x - 3) + 2x - 6 - 15
=> (g ° f)(x) = x² - 6x + 9 + 2x - 21
=> (g ° f)(x) = x² - 4x - 12
=> (g ° f)(x) = x² - 4x - 12
=> (g ° f)(-4) = (-4)² - 4(-4) - 12
=> (g ° f)(-4) = 16 + 16 - 12
=> (g ° f)(-4) = 32 - 12
=> (g ° f)(-4) = 20 => SAME ANSWER
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