Answer:
f(x) and g(x) are inverse functions
Step-by-step explanation:
In the two functions f(x) and g(x) if, f(g(x)) = g(f(x)) = x, then
f(x) and g(x) are inverse functions
Let us use this rule to solve the question
∵ f(x) = 3x²
∵ g(x) = 
→ Find f(g(x)) by substitute x in f(x) by g(x)
∴ f(g(x)) = 3()²
→ Cancel the square root with power 2
∴ f(g(x)) = 3(
)
→ Cancel the 3 up with the 3 down
∴ f(g(x)) = x
→ Find g(f(x)) by substitute x in g(x) by f(x)
∴ g(f(x)) = 
→ Cancel the 3 up with the 3 down
∴ g(f(x)) = 
→ Cancel the square root with power 2
∴ g(f(x)) = x
∵ f(g(x)) = g(f(x)) = x
→ By using the rule above
∴ f(x) and g(x) are inverse functions
Checking the <span>discontinuity at point -4
from the left f(-4) = 4
from the right f(-4) = (-4+2)² = (-2)² = 4
∴ The function is continues at -4
</span>
<span>Checking the <span>discontinuity at point -2
from the left f(-2) = </span></span><span><span>(-2+2)² = 0
</span>from the right f(-2) = -(1/2)*(-2)+1 = 2
∴ The function is jump discontinues at -2
</span>
<span>Checking the <span>discontinuity at point 4
from the left f(4) = </span></span><span><span>-(1/2)*4+1 = -1
</span>from the right f(4) = -1
but there no equality in the equation so,
</span><span>∴ The function is discontinues at 4
The correct choice is the second
point </span>discontinuity at x = 4 and jump <span>discontinuity at x = -2</span>
Answer:
2
Step-by-step explanation:
The answer is the second explanation I think
From the graph we observe:
If x = 0 then y = 1/2 (because e⁰ = 1)
Answer: X+10
X+10
Explanation:
Break down the information given to you to try and identify what the algebraic expression must looks like. You know that you're dealing with
a sum
→
this means that you are adding something, so you're going to use the
+
sign;
of a number
→
this means that you're dealing with a variable. The most common notation for a variable is
x
.
and 10
→
this is simply an integer that must appear in the algebraic expression along the variable
x
.
So, put all this together to get
x
+
10
You're adding an unknown number,
x
, to an integer,
10
