Exponential functions are related to logarithmic functions in that they are inverse functions. Exponential functions move quickly up towards a [y] infinity, bounded by a vertical asymptote (aka limit), whereas logarithmic functions start quick but then taper out towards an [x] infinity, bounded by a horizontal asymptote (aka limit).
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:

if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:

switch the x and y, then solve for y:

So the exponential function is the inverse of the logarithmic one, f(x) = ln x
20+64=84 40+44=84 74+10=84 30+54=84
Answer:
2
(
n
+
2
)
(
n
+
1
2
)
Step-by-step explanation:
coefficient of the first term:
2
=
2
×
1
coefficient of the last term:
2
=
2
×
1
coefficient of the middle term (using only the factors above):
5
=
2
×
2
+
1
×
1
2
n
2
+
5
n
+
2
=
(
2
n
+
1
)
(
n
+
2
)
Alternative method:
Treat the given expression as a quadratic set equal to zero, with the form
a
n
2
+
b
n
+
c
and use the quadratic formula
−
b
±
√
b
2
−
4
a
c
2
a
This will given solutions
n
=
−
2 and n
=
−
1
2
for a factoring
2
(
n
+
2
)
(
n
+
1
2
)
Hope this helped
Answer:
Step-by-step explanation:
let : y = x² - 8
calculate : x
x² = y + 8
x exist : y + 8 ≥ 0
x = √(y + 8) or x = - √(y + 8)
conclusion :
if : x ≥ 0 the inverse of f(x) is : g(x) = √(x + 8)
if : x ≤ 0 the inverse of f(x) is : h(x) = - √(x + 8)
Answer:
7
Step-by-step explanation:
1. Subtract the 4x on both sides = -14 = -2x
2. Divide -2 on both sides to get -14/-2 = x
3. -14/-2 = 7 so 7 = x