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MATH / If f(x), whose graph is shown below, is defined on 1≤x≤6, what is the maximum value of f^(−1)(x)? [asy] import graph; size(7.94cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10…

Problem

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problem

If f(x)f(x), whose graph is shown below, is defined on 1≤x≤61 \le x \le 6, what is the maximum value of f−1(x)f^{-1}(x)? [asy] import graph; size(7.94cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-0.96,xmax=8.96,ymin=-2.66,ymax=4.38; Label laxis; laxis.p=fontsize(10); xaxis("xx",-0.96,8.96,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis("yy",-2.66,4.38,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw((1,2)--(3,0),linewidth(1.2)); draw((3,3)--(5,2),linewidth(1.2)); draw((5,-2)--(6,0),linewidth(1.2)); filldraw(circle((5,-2),0.08),white); label("f(x) f(x) ",(0.5,4.3),SE*lsf); dot((3,0),UnFill(0)); dot((1,2)); dot((3,3)); dot((5,2),ds); dot((6,0)); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); [/asy]
Plain-text mathematical notation (without MathML)
If f(x), whose graph is shown below, is defined on 1≤x≤6, what is the maximum value of f^(−1)(x)? [asy]

import graph; size(7.94cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-0.96,xmax=8.96,ymin=-2.66,ymax=4.38;

Label laxis; laxis.p=fontsize(10);

xaxis("x",-0.96,8.96,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis("y",-2.66,4.38,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw((1,2)--(3,0),linewidth(1.2)); draw((3,3)--(5,2),linewidth(1.2)); draw((5,-2)--(6,0),linewidth(1.2)); filldraw(circle((5,-2),0.08),white); label("f(x)",(0.5,4.3),SE*lsf);

dot((3,0),UnFill(0)); dot((1,2)); dot((3,3)); dot((5,2),ds); dot((6,0));

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]
Original LaTeX notation
If $f(x)$, whose graph is shown below, is defined on $1 \le x \le 6$, what is the maximum value of $f^{-1}(x)$? [asy]

import graph; size(7.94cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-0.96,xmax=8.96,ymin=-2.66,ymax=4.38;

Label laxis; laxis.p=fontsize(10);

xaxis("$x$",-0.96,8.96,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); yaxis("$y$",-2.66,4.38,Ticks(laxis,Step=1.0,Size=2,OmitTick(0)),Arrows(6),above=true); draw((1,2)--(3,0),linewidth(1.2)); draw((3,3)--(5,2),linewidth(1.2)); draw((5,-2)--(6,0),linewidth(1.2)); filldraw(circle((5,-2),0.08),white); label("$ f(x) $",(0.5,4.3),SE*lsf);

dot((3,0),UnFill(0)); dot((1,2)); dot((3,3)); dot((5,2),ds); dot((6,0));

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]

level

Level 5

type

Algebra

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Source and history

task_id
bd508264-bfee-5a90-8a49-93b8211b7699
task_key
algebra--test--bd508264-bfee-5a90-8a49-93b8211b7699
task_revision_id
1
config / split
algebra / test

Official source

initial import