subject: Solve Exponential Function Domain [print this page] The exponential function in mathematics is defined as ex, where e is an integer. For example let us denote ex is an exponential function, Let us assume the value of x is zero, x = 0 then the solution is in the form of e0 = 1. Provided e.g. shows general concept of the exponential function. Now we are going to see about how to prepare for domain of the exponential function. Now we are going to solve exponential function domain.
Exponential Function Domain to Solve:
Exponent function of the domain to solve is nothing but the value of the function is lies between -infinity to +infinity.
To get review on domain exponential function,
First we have to start with the fundamental function of the exponential function of base a,
f (x) = ax , a > 0 and also not equal to 1.
Then the value of the domain function f is the set of all real numbers.
The range of f is the interval (0 , +infinity).
The given function have a horizontal asymptote which given by y = 0, then the function f has a y intercept at (0, 1).
When the value of the given function f is increased, then the value of a is greater than 1
When the value of the given function f is decreased, then the value of a is lesser than 1
Example to Solve Exponential Function Domain:
Example to solve exponential function domain 1:
Calculate the domain and range of f from the given function f (x) = 2(x - 2), .
Solution:
Step 1: The given function is f (x) = 2(x + 2)
Step 2: We know that the domain of the Exponential function f, which is the set of all real numbers.
Step 3: To find the range of the given function f, we have to starts with '2^x ''> 0'
Multiply 2+2 on both sides, which is positive.
2x 22 > 0
Use exponential properties
'2^(x + 2) ' > 0
Thus the obtained result tells that f(x) > 0.The range of f is (0, +infinity).
Example to solve exponential function domain 2:
Calculate the domain and range of f from the given function f (x) = 3(x - 5) - 8.
Solution:
Step 1: The given function is f (x) = 3(x - 5) - 8
Step 2: We know that the domain of the Exponential function f, which is the set of all real numbers.
Step 3: To find the range of the given function f, we have to starts with 3x > 0
Multiply by 3-5 on both sides
3x 3-5> 0
By using exponential properties
3(x - 5) > 0
Subtract 8 to both side we may get,
3(x - 5) -8 > -8
Thus the obtained solution describe that f(x) > -8. The range of f is (-8, +inf).
