When is #g(x)=0# for the function #g(x)=5*2^(3x)+4#?

2 Answers
Alan P.
Nov 8, 2016

If #g(x)=5 * 2^(3x)+4#
then #g(x)# is never #=0#

Explanation:

For any positive value #k# and any Real value #p#
#color(white)("XXX")k^p > 0#

Therefore
#color(white)("XXX")2^(3x) > 0# for #AAx in RR#

and
#color(white)("XXX")rarr 5*2^(3x) > 0# for #AAx in RR#

and
#color(white)("XXX")rarr 5*2(3x)+4 > 0# for #AAx in RR#

Monzur R.
Nov 8, 2016

For this function, #g(x) != 0#.

Explanation:

This is an exponential function, and, generally, exponential functions have no #y#-value equal to #0#. This is because no exponent of any number will give you #0# (or anything smaller than it).

The only way to have an exponential function which intercepts the #x#-axis is the translate the graph downwards.

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