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 ) Encounter graph of f beneath and examine the range graphically. Matched Trouble 4: Find the range of office f defined by Answers to Matched Problems 1. (0 , +∞) 2. (-∞ , -2) iii. (-∞ , -6] 4. (-seven , -3] More References and Links Find the domain of a function mathematics tutorials and problems.

Source: https://www.analyzemath.com/DomainRange/find_range_exponential.html

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