General approach of exponential functions, Mathematics

Assignment Help:

General approach of Exponential Functions :Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential function is a function in the form,

                                       f( x ) = b x

Note that we avoid b = 1 since that would give the constant function, f( x ) = 1 .  We ignore

b= 0 as this would also give a constant function and we ignore negative values of b for the following cause. Let's, for a second, assume that we did let b to be negative and look at the given function.

                                        g( x ) = ( -4)x

Let's perform some evaluation.

g( 2)= ( -4)2 =16            g (1/2) =  ( -4)2   =√   -4 = 2i

hence, for some values of x we will obtain real numbers and for other values of x well we get complex numbers.  We desire to avoid this and thus if we require b = 0 this will not be a problem.


Related Discussions:- General approach of exponential functions

How far off shore is the sinking ship, A sinking ship signals to the shore ...

A sinking ship signals to the shore for assistance. Three individuals spot the signal from shore. The ?rst individual is directly perpendicular to the sinking ship and 20 meters in

Find the area of shaded region of circle of radius, Find the area of shaded...

Find the area of shaded region of circle of radius =7cm, if ∠AOB=70 o , ∠COD=50 o and ∠EOF=60 o . (Ans:77cm 2 ) Ans:    Ar( Sector AOB + Sector COD + Sector OEF) =  7

Differential Equations, Find the normalized differential equation which has...

Find the normalized differential equation which has { x, xe^x } as its fundamental set

Quantitative analysis, Suppose the economy is now ‘open’ and thus has an ex...

Suppose the economy is now ‘open’ and thus has an external demand (e.g. from the government, exports, etc.) of the dollar amounts for each respective industry. In the latest budget

Hieght and distances, A boy standing in the middle of a field, observes a f...

A boy standing in the middle of a field, observes a flying bird in the north at an angle of elevation fo 30 degree. and after 2 min, he observes the same bird in the south at an an

Angles, samuel left mauritius at 22:30 on saturday and travelled to london ...

samuel left mauritius at 22:30 on saturday and travelled to london (GMT) for 14h30min he had a stopover for 4 h in london and he continued to travel to toronto for another 6h20min

Differential equations, Verify Liouville''''s formula for y "-y" - y'''' + ...

Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?

Inverse functions, Inverse Functions : In the last instance from the pr...

Inverse Functions : In the last instance from the previous section we looked at the two functions   f ( x ) = 3x - 2 and g ( x ) = x /3+ 2/3 and saw that ( f o g ) ( x )

Solid mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd