What is the range of #f(x) = -3^x + 4#?

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Answer 1 · 2015-05-06T16:50:21

Write #y=-3^x+4#

#=>3^x=4-y#

Take #ln# of both sides

#=>ln3^x=ln(4-y)#

#=>x=ln(4-y)/ln3#

Now notice that #(4-y)# cannot be negative nor zero!

#=>4-y>0 =>y<4#

Hence the range of #f(x)# is #f(x)<4#