Evaluating functions
Given the function; w(t) = −2t + 1
Find w(−7)
w(−7)= -2(-7) +1
= 14+1
=15
Given the Functions, f(x) = 2x+3 and g(x) = x2
What is g(f(0))?
g(f(0)) = (2(0) +3)2
= (0 +3)2
= (3)2
= 9
Given the piecewise functions
g(x) = 3x +5 -2r if x < 2
x3 +7 if x>2
at what value of x will the function be continuous
3x +5 -2r = x3 + 7
3(2) +5 -2r = (2)3 +7
6 +5 - 2r = 8 +7
11 - 2r = 15
-2r = 4
r = -2
Given the function f(x) = 3x -4
What is f(f(x))
f(f(x)) = 3(3x - 4) - 4
= 9x - 12 - 4
= 9x -16
Given the function f(x) = x2 +2x - 4
What is f(3)
f(3) = 32 +2(3) - 4
= 9 +6 -4
= 15 - 4
= 11
Given the function g(a) = 3 3a − 2
Find g(1)
g(1) = 3 3(1) − 2
= 3 3 − 2
= 3 1
= 3
Given the functions h(x) = 2x - 6 and g(x) = x+ 4
What is h(g(x))
h(g(x)) = 2(x+4) - 6
= 2x +8 -6
= 2x + 2
Given the f(x) = 3x - 4 and g(x) = x3+ 9
fg(2)
fg(2)= 3((22)+9) -4
= 3(4+9) -4
= 3(13) - 4
= 39 - 4
= 35
Given the functions g(n) = n + 1 f (n) = n 2 - n
Find g( f (8))
g(f(8)) = ((82) -8) +1
= (64 - 8) +1
= (56)+1
=57
Given the functions f(x) x2 and g(x) = x -4
What is g(f(x))? Fully simplify your answer.
g(f(x)) = (x2) - 4
= x2 - 4
Given the functions f(x) 2x -10 and g(x) 3x2
What is (f + g)(5)
(f - g)(5) = f(5) - g(5)
= 2(5) -10 - (3(25))
= 10 -10 -75
= -75
Given the following functions
g(x) = 3x + 3 f (x) =x3 - 3x 2
Find g( f (x))= 3(x3 - 3x 2) + 3
= 3x3 - 9x 2 +3
Given f(x) = x2 and g(x) = x - 4
What is f(g(x))? Fully simplify your answer
f(g(x)) = (x - 4)2
=(x -4) (x - 4)
= x2 -4x -4x +16
= x2 -8x +16
If h(x) = 4x2 -9x +5 and h(1) = 0
What is the value of h(0.5)
h(0.5) = 4(0.5)2 -9(0.5) +5
= 4(0.25) - 4.5 +5
= 1 - 4.5 +5
= -3.5 +5
= 1.5
Given the functions g(x) = 4x + 5 Find
g(g( x /3 ))
g(g( x /3 )) = 4(4(x/3)+5)
=4(4x/3 +5) +5
= 16x/3 +20 +5
= 16x/3 +25
= (16x +75) / 3
Given the functions f(x) = x+2 g(x) = 3x and h(x) = x2 +3x -4
What is h(g(fx))
h(g(fx)) = (3(x+2))2 +3(3(x+2)) -4
= (3x +6)2 + 3(3x +6) -4
= 9x2 +36x +36 +9x +18 -4
= 9x2 +45x +50