How To Find The Range Of An Exponential Function

Detect Range of Exponential Functions

Detect the range of existent valued exponential functions using different techniques. Matched issues are also included with their answers at the bottom of the page.

Examples with Solutions

Example i

Detect the Range of function f defined by

Solution to Instance 1

Matched Trouble one:

Detect the range of office f defined by

Instance 2

Find the Range of part f defined by

Solution to Example 2

Matched Problem 2:

Find the range of part f defined past

Example 3

Find the Range of role f defined past

Solution to Example 3

Write the given function every bit an equation
Solve the above for x to obtain
x² = ln(y - i)
x = + or - √[ ln(y - ane) ]
The above solutions are existent if
ln(y - 1) ≥ 0
y - 1 ≥ ane
y ≥ 2
Hence the range of the given part is given past
y ≥ 2 or in interval course [ two , + ∞ )

Encounter graph of f below and examine the range graphically.

Matched Problem 3:

Detect the range of function f defined by

Example 4

Discover the Range of part f defined by

Solution to Example 4

We first write the given function as an equation every bit follows
Solve the above for x
y - three = -two e^-x²
e^-10² = (y - 3) / (-2)
-x² = ln [ (y - 3) / (-2) ]
x = + or - √( - ln [ (y - 3) / (-2) ])
10 is existent if the argument of ln is positive and the radicand is positive or zero. Hence the following inequalities
(y - 3) / (-2) > 0 and - ln [ (y - iii) / (-two) ] ≥ 0
the solution set of (y - iii) / (-two) > 0 is y < 3
the solution set of - ln [ (y - three) / (-2) ] ≥ 0 is given past (y - 3) / (-2) ≤ 1 which gives y ≥ 1
the range of f is given by
1 ≤ y < three or in interval class [ 1 , iii )