Evaluate Functions
Evaluate the following function:
f(5) = x2 + 3x - 25
15
Evaluate and elaborate the compound functions:
h(x)=4
g(x)= 1 + √(x)
g(h(x)) =
3
Decompose f(g(x)) into f(x) and g(x).
f(g(x)) = 9 / ( x - 6 )
g(x) = x - 6
f(x) = 9 / x
Find the inverse function of:
f(x) = 2x + 8
f-1(x) = ( x - 8 ) / 2
We can solve negative square roots.
FALSE.
Negative square roots have an undefined value.
Evaluate the following function:
f(5) = 3x+12
27
Evaluate and elaborate the compound functions:
a(x) = 3x +12
b(x) = x2
b(a(x)) =
9x2 + 72x + 144
(3x + 12)2
Decompose f(g(x)) into f(x) and g(x).
f(g(x)) = (2x - 1)2
f(x) = x2
g(x) = 2x - 1
Find the inverse function of:
f(x) = x2 - 5
f-1(x) = √(x+5)
It is not possible to divide by zero.
TRUE.
Division by zero is an undefined value.
Evaluate the following function:
b(4) = √(x) / 2
1
Evaluate and elaborate the compound functions:
a(x) = 2x - 3
b(x) = 2x2
b(a(X)) =
8x2 - 24x +18
2(2x-3)2
Decompose f(g(x)) into f(x) and g(x).
f(g(x)) = (x - 2) / 4
g(x) = x - 2
f(x) = x / 4
Find the inverse function of:
f(x) = √(x -2)
f-1(x) = x2 + 2
(f-1o f)(-3) = 4
FALSE
The result is -3.
Evaluate the following function:
c(6) = (4 + X2 ) / 4
10
Evaluate and elaborate the compound functions:
f(x) = 3x + 5
f(f(x)) =
9x + 20
Decompose f(g(x)) into f(x) and g(x).
f(g(x)) = 7 - 2 / √(x)
g(x) = √(x)
f(x) = (7-2) / x
Find the inverse function of:
f(x) = √(x+2) - 4
f-1(x) = (x+4)2 - 2
or
x2 - 8x + 14
The Domain of f is different to the Range of f-1.
FALSE
It is the same.
Evaluate the following function:
a(2) = ( 3x - 1 ) / (2x + 6)
1/2, 0.5
Evaluate and elaborate the compound functions:
f(x) = 4x + 3
b(x) = x2
b(f(x)) =
16x2 + 24x + 9
(4x + 3)2
Decompose f(g(x)) into f(x) and g(x).
f(g(x)) = √(x + 1) / 2
f(x) = x / 2
g(x) = √(x + 1)
Find the inverse function of:
f(x) = (-x + 6 ) / (5 + 3x)
f-1(x) = (6 - 5x) / (3x + 1)
If f and f-1 are inverses of each other then their graphs are reflections of each other on the line x-axis.
They are reflected across y = x.